Acta Stereologica

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Konrad Sandau & Haymo Kurz

A 2-D model for the growth of arteries

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Abstract

This study is based on observations of the growth of arteries and capillary networks in the chorioallantoic membrane (CAM) of incubated chicken eggs. The structure of the capillary layer can be described as a planar, area-filling hexagonal grid, whereas the arteries are seen in a plane underneath the capillary plexus, resembling a bifurcating vessel tree. Further biological observations strongly suggest that the larger vessels do not form sprouts but that they exclusively originate from capillary proliferation and enlargement. A model for this mechanism of blood vessel formation has been developed and compared with anatomical and physiological data.

In a computer simulation, growth of the network is driven by a stochastic process starting in a point source. The probabilities for the formation of new capillary elements are derived from the flow theorem of Hagen-Poiseuille and the diameter exponent. The hexagonal grid is visualized as being supported by a flat limited area, a cylinder, and a sphere. The time course of growth and of blood pressure is obtained. The resulting arterial tree is considered to have limited fractal properties, and the dimension of its border is compared with the biological data.

Keywords : angiogenesis, blood vessel, chorioallantoic membrane, computer simulation, development, diameter exponent, fractal, Hagen-Poiseuille, stochastic process

To cite this article

Konrad Sandau & Haymo Kurz, «A 2-D model for the growth of arteries», Acta Stereologica [En ligne], Volume 12 (1993), Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993, 141-148 URL : https://popups.ulg.ac.be/0351-580x/index.php?id=1743.

About: Konrad Sandau

FB Mathematik der Fachhochschule, Schöfferstr. 3, D-64295 Darmstadt

About: Haymo Kurz

Anatomisches Institut II des Universität, Albertstr. 17, D-79001 Freiburg